Spin and valley filter in strain engineered silicene

The realization of a perfect spin or valley filtering effect in two-dimensional graphene-like materials is one of the fundamental objectives in spintronics and valleytronics. For this purpose, we study spin- and valley-dependent transport in a silicene system with spatially alternative strains. It is found that due to the valley-opposite gauge field induced by the strain, the strained silicene with a superlattice structure exhibits an angle-resolved valley and spin filtering effect when the spin–orbit interaction is considered. When the interaction that breaks the time reversal symmetry is introduced, such as the spin or valley dependent staggered magnetization, the system is shown to be a perfect spin and valley half metal in which only one spin and valley species is allowed to transport. Our findings are helpful to design both spintronic and valleytronic devices based on silicene.     

Spin and valley half metal induced by staggered potential and magnetization in silicene

We investigate the electron transport in silicene with both staggered electric potential and magnetization; the latter comes from the magnetic proximity effect by depositing silicene on a magnetic insulator. It is shown that the silicene could be a spin and valley half metal under appropriate parameters when the spin–orbit interaction is considered; further, the filtered spin and valley could be controlled by modulating the staggered potential or magnetization. It is also found that in the spin-valve structure of silicene, not only can the antiparallel magnetization configuration significantly reduce the valve-structure conductance, but the reversing staggered electric potential can cause a high-performance magnetoresistance due to the spin and valley blocking effects. Our findings show that the silicene might be an ideal basis for the spin and valley filter analyzer devices.     

Quantum spin Hall and quantum valley Hall effects in trilayer graphene and their topological structures

The present study pertains to the trilayer graphene in the presence of spin orbit coupling to probe the quantum spin/valley Hall effect. The spin Chern-number C_s for energy-bands of trilayer graphene having the essence of intrinsic spin–orbit coupling is analytically calculated. We find that for each valley and spin, C_s is three times larger in trilayer graphene as compared to single layer graphene. Since the spin Chern-number corresponds to the number of edge states,consequently the trilayer graphene has edge states, three times more in comparison to single layer graphene. We also study the trilayer graphene in the presence of both electric-field and intrinsic spin–orbit coupling and investigate that the trilayer graphene goes through a phase transition from a quantum spin Hall state to a quantum valley Hall state when the strength of the electric field exceeds the intrinsic spin coupling strength. The robustness of the associated topological bulk-state of the trilayer graphene is evaluated by adding various perturbations such as Rashba spin–orbit(RSO) interaction αR, and exchange-magnetization M. In addition, we consider a theoretical model, where only one of the outer layers in trilayer graphene has the essence of intrinsic spin–orbit coupling, while the other two layers have zero intrinsic spin–orbit coupling.Although the first Chern number is non-zero for individual valleys of trilayer graphene in this model, however, we find that the system cannot be regarded as a topological insulator because the system as a whole is not gaped.     

Electrical controllable spin valves in a zigzag silicene nanoribbon ferromagnetic junction

We propose two possible spin valves based on a zigzag silicene nanoribbon(ZSR) ferromagnetic junction. By using the Landauer–B u¨tikker formula, we calculate the spin-resolved conductance spectrum of the system and find that the spin transport is crucially dependent on the band structure of the ZSR tuned by a perpendicular electric field. When the ZSR is in the topological insulator phase under a zero electric field, the low-energy spin transport and its ON and OFF states in the tunneling junction mainly rely on the valley valve effect and the edge state of the energy band, which can be electrically modulated by the Fermi level, the spin–orbit coupling, and the local magnetization. When a nonzero perpendicular electric field is applied, the ZSR is a band insulator with a finite energy gap, the spin switch phenomenon is still preserved in the device and it does not come from the valley valve effect, but from the energy gap opened by the perpendicular electric field. The proposed device might be designed as electrical tunable spin valves to manipulate the spin degree of freedom of electrons in silicene.     

Ground state of rotating ultracold quantum gases with anisotropic spin orbit coupling and concentrically coupled annular potential

Motivated by recent experimental realization of synthetic spin–orbit coupling in neutral quantum gases, we consider the quasi-two-dimensional rotating two-component Bose–Einstein condensates with anisotropic Rashba spin–orbit coupling subject to concentrically coupled annular potential. For experimentally feasible parameters, the rotating condensate exhibits a variety of rich ground state structures by varying the strengths of the spin–orbit coupling and rotational frequency.Moreover, the phase transitions between different ground state phases induced by the anisotropic spin–orbit coupling are obviously different from the isotropic one.     

Composite solitons in SU(3) spin–orbit-coupling Bose gases

We study solitons in a spin-1 Bose–Einstein condensates with SU(3) spin–orbit coupling. We obtain the ground state and the metastable solution for solitons with attractive interactions by the imaginary-time evolution method. Compared with the SU(2) spin–orbit coupling, it is found that the solitons in SU(3) spin–orbit coupling show a new feature due to breaking the symmetry. The solitons called the composite solitons have mixing manifolds of ferromagnetic and antiferromagnetic states. This has stimulated people to study the topological excitation properties of SU(3) spin–orbit coupling and it is expected to find new quantum phases.     

Current-induced nonequilibrium spin polarization in semiconductor-nanowire/s-wave superconductor junctions with strong spin–orbit coupling

We have studied the characteristics of current-induced nonequilibrium spin polarization in semiconductor-nanowire/swave superconductor junctions with strong spin–orbit coupling. It was found that within some parameter regions the magnitude of the current-induced nonequilibrium spin polarization density in such structures will increase(or decrease) with the decrease(or increase) of the charge current density, in contrast to that found in normal spin–orbit coupled semiconductor structures. It was also found that the unusual characteristics of the current-induced nonequilibrium spin polarization in such structures can be well explained by the effect of the Andreev reflection.     

Topological superfluid in a two-dimensional polarized Fermi gas with spin-orbit coupling and adiabatic rotation

We study the properties of superfluid in a two-dimensional(2 D) polarized Fermi gas with spin–orbit coupling and adiabatic rotation which are trapped in a harmonic potential. Due to the competition between polarization, spin–orbit coupling, and adiabatic rotation, the Fermi gas exhibits many intriguing phenomena. By using the Bardeen–Cooper–Schrieffer(BCS) mean-field method with local density approximation, we investigate the dependence of order parameter solution on the spin–orbit coupling strength and the rotation velocity. The energy spectra with different rotation velocities are studied in detail. Besides, the conditions for the zero-energy Majorana fermions in topological superfluid phase to be observed are obtained. By investigating distributions of number density, we find that the rotation has opposite effect on the distribution of number density with different spins, which leads to the enhancement of the polarization of Fermi gas. Here,we focus on the region of BCS pairing and ignore the Fulde–Ferrell–Larkin–Ovchinnikov state.     

Spin and valley half metal induced by staggered potential and magnetization in siliceneSpin and valley half metal induced by staggered potential and magnetization in siliceneSpin and valley half metal induced by staggered potential and magnetization in silicene

We investigate the electron transport in silicene with both staggered electric potential and magnetization; the latter comes from the magnetic proximity effect by depositing silicene on a magnetic insulator. It is shown that the silicene could be a spin and valley half metal under appropriate parameters when the spin-orbit interaction is considered; further, the filtered spin and valley could be controlled by modulating the staggered potential or magnetization. It is also found that in the spin-valve structure of silicene, not only can the antiparallel magnetization configuration significantly reduce the valve-structure conductance, but the reversing staggered electric potential can cause a high-performance magnetoresistance due to the spin and valley blocking effects. Our findings show that the silicene might be an ideal basis for the spin and valley filter analyzer devices.     

Thermodynamic behaviour of Rashba quantum dot in the presence of magnetic field

The thermodynamic properties of an In Sb quantum dot have been investigated in the presence of Rashba spin–orbit interaction and a static magnetic field. The energy spectrum and wave-functions for the system are obtained by solving the Schrodinger wave-equation analytically. These energy levels are employed to calculate the specific heat, entropy,magnetization and susceptibility of the quantum dot system using canonical formalism. It is observed that the system is susceptible to maximum heat absorption at a particular value of magnetic field which depends on the Rashba coupling parameter as well as the temperature. The variation of specific heat shows a Schottky-like anomaly in the low temperature limit and rapidly converges to the value of 2kB with the further increase in temperature. The entropy of the quantum dot is found to be inversely proportional to the magnetic field but has a direct variation with temperature. The substantial effect of Rashba spin–orbit interaction on the magnetic properties of quantum dot is observed at low values of magnetic field and temperature.     

Assessment of bilayer silicene to probe as quantum spin and valley Hall effect

Silicene takes precedence over graphene due to its buckling type structure and strong spin orbit coupling. Motivated by these properties, we study the silicene bilayer in the presence of applied perpendicular electric field and intrinsic spin orbit coupling to probe as quantum spin/valley Hall effect. Using analytical approach, we calculate the spin Chern-number of bilayer silicene and then compare it with monolayer silicene. We reveal that bilayer silicene hosts double spin Chern-number as compared to single layer silicene and therefore accordingly has twice as many edge states in contrast to single layer silicene. In addition, we investigate the combined effect of intrinsic spin orbit coupling and the external electric field, we find that bilayer silicene, likewise single layer silicene, goes through a phase transitions from a quantum spin Hall state to a quantum valley Hall state when the strength of the applied electric field exceeds the intrinsic spin orbit coupling strength. We believe that the results and outcomes obtained for bilayer silicene are experimentally more accessible as compared to bilayer graphene, because of strong SO coupling in bilayer silicene.     

Spin and valley dependent line-type resonant peaks in electrically and magnetically modulated silicene quantum structures

A barrier with a tunable spin-valley dependent energy gap in silicene could be used as a spin and valley filter. Meanwhile, special resonant modes in unique quantum structure can act as energy filters. Hence we investigate valley and spin transport properties in the potential silicene quantum structures, i.e., single ferromagnetic barrier, single electromagnetic barrier and double electric barriers. Our quantum transport calculation indicates that quantum devices of high accuracy and efficiency (100% polarization), based on modulated silicene quantum structures, can be designed for valley, spin and energy filtering. These intriguing features are revealed by the spin, valley dependent line-type resonant peaks. In addition, line-type peaks in different structure depend on spin and valley diversely. The filter we proposed is controllable by electric gating.     

Quantum spin Hall effect in silicene and two-dimensional germanium

We investigate the spin-orbit opened energy gap and the band topology in recently synthesized silicene as well as two-dimensional low-buckled honeycomb structures of germanium using first-principles calculations. We demonstrate that silicene with topologically nontrivial electronic structures can realize the quantum spin Hall effect (QSHE) by exploiting adiabatic continuity and the direct calculation of the Z(2) topological invariant. We predict that the QSHE can be observed in an experimentally accessible low temperature regime in silicene with the spin-orbit band gap of 1.55 meV, much higher than that of graphene. Furthermore, we find that the gap will increase to 2.9 meV under certain pressure strain. Finally, we also study germanium with a similar low-buckled stable structure, and predict that spin-orbit coupling opens a band gap of 23.9 meV, much higher than the liquid nitrogen temperature.     

门电压控制的硅烯量子线中电子输运性质

硅烯是由单层硅原子形成的二维蜂窝状晶格结构,具有石墨烯类似的电学性质,由于硅烯中存在比较强的自旋轨道耦合而备受关注.本文利用非平衡格林函数方法研究了门电压控制的硅烯量子线中电子输运性质和能带结构.研究发现,只有在较强的门电压下,而且硅烯量子线具有较好的锯齿形或扶手椅形边界而不存在额外硅原子时,硅烯量子线中才存在无能隙的自旋极化边缘态.另外,计算结果表明这种门电压控制的硅烯量子线中边缘态在每个能谷处自旋是极化的.这些计算结果将为实验上利用电场制作硅烯纳米结构提供理论支持.     

Rashba spin-orbit effect on dwell time of electrons tunneling through semiconductor barrier

A study on characteristics of electrons tunneling through semiconductor barrier is evaluated, in which we take into account the effects of Rashba spin-orbit interaction. Our numerical results show that Rashba spin-orbit effect originating from the inversion asymmetry can give rise to the spin polarization. The spin polarization does not increase linearly but shows obvious resonant features as the strength of Rashba spin-orbit coupling increases, and the amplitudes of spin polarization can reach the highest around the first resonant energy level. Furthermore, it is found that electrons with different spin orientations will spend quite different time through the same heterostructures. The difference of the dwell time between spin-up and spin-down electrons arise from the Rashba spin-orbit coupling. And it is also found that the dwell time will reach its maximum at the first resonant energy level. It can be concluded that, in the time domain, the tunneling processes of the spin-up and spin-down electrons can be separated by modulating the strength of Rashba spin-orbit coupling. Study results indicate that Rashba spin-orbit effect can cause a nature spin filter mechanism in the time domain.     

Silicene on substrates:A theoretical perspective

Silicene, as the silicon analog of graphene, is successfully fabricated by epitaxially growing it on various substrates.Like free-standing graphene, free-standing silicene possesses a honeycomb structure and Dirac-cone-shaped energy band,resulting in many fascinating properties such as high carrier mobility, quantum spin Hall effect, quantum anomalous Hall effect, and quantum valley Hall effect. The existence of the honeycomb crystal structure and the Dirac cone of silicene is crucial for observation of its intrinsic properties. In this review, we systematically discuss the substrate effects on the atomic structure and electronic properties of silicene from a theoretical point of view, especially with emphasis on the changes of the Dirac cone.     

磁性硅烯超晶格中电场调制的谷极化和自旋极化

研究了基于硅烯的静电势超晶格、铁磁超晶格、反铁磁超晶格中谷极化、自旋极化以及赝自旋极化的输运性质,分析了铁磁交换场、反铁磁交换场以及化学势对输运性质的影响,讨论了电场对谷极化、自旋极化以及赝自旋极化的调控作用.结果表明:当3种超晶格的晶格数达到10以上时,在硅烯超晶格中很容易实现100%的谷极化、自旋极化和赝自旋极化,而且通过调节超晶格上的外加电场可以使极化方向发生翻转,从而在硅烯超晶格中实现外电场对谷自由度、自旋自由度以及赝自旋自由度的操控.     

Spin Polarizations of Electron with Rashba Couplings in T-Shaped Devices: A Finite Element Approach

A generalized finite element formulation is proposed for the study of the spin-dependent ballistic transport of electron through the two-dimensional quantum structures with Rashba spin-orbit interactions (SOI). Thetransmission coefficient, conductance, the total and local polarization are numerically calculated and discussed as the Rashba coefficient, the geometric sizes, and incident energy are changed in the T-shaped devices. Some interesting features are found in the proper parameter regime. The polarization has an enhancement as the Rashba coefficient becomes stronger. The polarization valley is rigid in the regime of the conductance plateaus since the local interference among the polarized multi-wave modes. The Rashba interactions coupling to geometry in sizes could form the structure-induced Fano-Rashba resonance. In the wider stub, the localized spin lattice of electron could be produced. The conductance plateaus correspond to weakpolarizations. Strong polarizations appear when the stub sizes, incident energy, and the Rashba coupling coefficient are matched. The resonances are formed in a wide Fermi energy segment easily.